Number Triangles
corner + corner = side

Play Number Triangles

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Tap a circle, then type

How to play Number Triangles

Each shape has a number at every corner and a number on every side. The side number is always the sum of the two corners at its ends.

Some numbers are hidden. When you know a side and one of its corners, subtract to find the other corner. When only the sides are shown, a little more thinking is needed: in a triangle, add up all three sides and halve it — that is the total of the three corners.

These puzzles are sometimes called arithmagons. They are a lovely way to practise addition, subtraction and a first taste of algebra.

How to play Number Triangles

Each side number is the sum of the two corners next to it — find the hidden corners and sides.

The rules

  1. There is a number at every corner and on every side.
  2. Each side number is the sum of the two corners at its ends.
  3. Some numbers are hidden. Fill them all in.
  4. Every puzzle has exactly one answer.

Playing here

  1. Choose a shape (triangle, square or pentagon) and a difficulty, then press New Puzzle.
  2. The number on each side is the sum of the two corners at its ends.
  3. Tap a circle and type a number. Find every missing corner and side.
  4. Hint shows the next number you can work out, and the sum that gives it.

Tips

The full guide, with a worked example and common mistakes: How to play Number Triangles.

Questions

Why doesn’t the square have the halving trick?

In a square, the sides cannot tell you the corners on their own — so square puzzles always show at least one corner.

Are negative numbers used?

No — all the numbers are whole numbers of at least 1.

Is there always one answer?

Yes — every puzzle is checked to have exactly one answer.

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